Biomedical Engineering Reference
In-Depth Information
the optical properties, start to change. The change in properties in turn influences the pro-
cess of energy absorption and distribution in the tissue.
The next stage in these processes is the onset of ablation. As the temperature continues to
rise, a threshold temperature is reached, at which point, if the rate of heat deposition con-
tinues to exceed the rate at which the tissue can transport the energy, an intensive process
of vaporization of the water content of the tissue combined with pyrolysis of tissue macro-
molecules initiates, which results in ablation or removal of tissue.
17.5.1 Temperature Field during Light/Laser Coagulation
In this section the governing equations are described for a thermodynamic analysis of
light heating of biological tissues up to the onset of ablation. First, the heat conduction
equation and typical boundary and initial conditions are described. Next the Arrhenius-
Henriques model for quantitative analysis of irreversible thermal injury to biological tissue
will be introduced.
Section 17.2 discussed how light energy is absorbed by a participating medium such as
biological tissue. As light energy with a rate
is absorbed by a material under irradiation,
there is an immediate thermal energy flux traveling in different directions. This is caused by
nonuniformity of
Q
L
in both the radial direction, due to beam profile, and the axial direc-
tion, due to absorption. The energy rate balance equation in the material can be found as
follows.
Consider an infinitesimal element of
Q
L
the material under
light/laser
irradiation
(Figure 17.14). The rate of thermal energy storage in the element,
, depends on the dif-
ference between incoming and outgoing thermal fluxes, the rate of light energy absorp-
tion,
U
Q
o
. The
difference between influx and efflux is, in the limit, equal to the negative of the divergence
of the thermal flux vector. So the energy rate balance can be written as
Q
L
, and other energy rate interactions that are lumped together and labeled
@
U
=@
t
¼r~
q
þ
Q
L
þ
Q
o
ð
17
:
69
Þ
q
in
(rate of heat generated
by the laser)
Q
L
U
(r)
Q
o
q
out
FIGURE 17.14
Thermal fluxes and energy in a control volume in the “material phase.”
